¼ cup plus 2 tablespoons olive oil, plus more to drizzle
½ teaspoon kosher salt
½ pound boneless, skinless salmon fillet, cut into 1-inch cubes
1 red onion, halved and thinly sliced
2 garlic cloves, chopped
1 pound cherry tomatoes (about 1 ½ pints), halved
½ cup dry white wine, such as Pinot Grigio
1 ½ cups mixed pitted olives, halved if large
2 teaspoons fresh oregano leaves, chopped
¾ cup fresh flat-leaf parsley leaves, chopped
1 cup freshly grated Parmigiano-Reggiano, plus more for serving
Bring a large pot of water to a boil. Season the water generously with kosher salt. Add the pasta and cook for 2 minutes less than directed on the package, about 5 minutes.
Reserve ½ cup of the pasta cooking water, then drain the pasta. If using gluten-free pasta, rinse it well under cool running water, then drain again. While the pasta cooks, heat large skillet over medium-high heat.
Add 2 tablespoons of olive oil. Season the salmon evenly with ¼ teaspoon of the salt and place in the hot pan.
Cook the fish cubes without moving them for 2 to 3 minutes, or until golden brown on the first side. Add the onion and garlic and cook, stirring often, for another minute.
Add the tomatoes and season with the remaining ¼ teaspoon salt.Cook the tomatoes, stirring often, for another 3 minutes, or until beginning to soften. By this point the salmon will be flaking apart a bit, but try to keep it in larger pieces to prevent it from drying out too much.
Reduce the heat to medium and stir in the white wine, scraping the pan to loosen any brown bits. Simmer for 2 minutes to reduce slightly, then stir in the olives, oregano, parsley.
Add the pasta to the pan and sprinkle with the cheese. Toss to coat. Add ¼ cup of the reserved pasta cooking water and the remaining ¼ cup oil and toss to combine.
Add more pasta water as needed to create a silky sauce.
Serve with additional cheese and olive oil, if desired.